Meaning "point of the chin" is pugilistic slang, by 1921. A button as something you push to create an effect by closing an (electrical) circuit is attested from 1840s. Button-pusher as "deliberately annoying or provocative person" is attested by 1990 (in reference to Bill Gates, in "InfoWorld" magazine, Nov. 19). In the 1980s it meant "photographer."

v.

late 14c., "to furnish with buttons;" early 15c., "to fasten with buttons" (of a garment,) from button (n.) or from Old French botoner (Modern French boutonner), from boton (n.). Related: Buttoned; buttoning. Button-down (adj.) in reference to shirt collars is from 1916.